On group feedback vertex set parameterized by the size of the cutset

Abstract

We study parameterized complexity of a generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem: we are given a graph G with edges labeled with group elements, and the goal is to compute the smallest set of vertices that hits all cycles of G that evaluate to a non-null element of the group. This problem generalizes not only Feedback Vertex Set, but also Subset Feedback Vertex Set, Multiway Cut and Odd Cycle Transversal. Completing the results of Guillemot [Discr. Opt. 2011], we provide a fixed-parameter algorithm for the parameterization by the size of the cutset only. Our algorithm works even if the group is given as a blackbox performing group operations. © 2012 Springer-Verlag Berlin Heidelberg.